Hierarchical decision-making is a natural paradigm for coordinating multi-agent systems in complex environments such as air traffic management. In this paper, we present a bilevel framework for game-theoretic hierarchical routing, where a high-level router assigns discrete routes to multiple vehicles who seek to optimize potentially noncooperative objectives that depend upon the assigned routes. To address computational challenges, we propose a reformulation that preserves the convexity of each agent's feasible set. This convex reformulation enables a solution to be identified efficiently via a customized branch-and-bound algorithm. Our approach ensures global optimality while capturing strategic interactions between agents at the lower level. We demonstrate the solution concept of our framework in two-vehicle and three-vehicle routing scenarios.
@article{arxiv.2503.13790,
title = {A Convex Formulation of Game-theoretic Hierarchical Routing},
author = {Dong Ho Lee and Kaitlyn Donnel and Max Z. Li and David Fridovich-Keil},
journal= {arXiv preprint arXiv:2503.13790},
year = {2025}
}